Jörn Dunkel

Nonreciprocal interactions—where forces between entities are asymmetric—govern a wide range of nonequilibrium phenomena, yet their role in structural transitions in living and active systems remains elusive. Here, we demonstrate a transition between nonreciprocal states using starfish embryos at different stages of development, where interactions are inherently asymmetric and tunable. Experiments, interaction inference, and topological analysis yield a nonreciprocal state diagram spanning crystalline, flock-like, and fragmented states, revealing that weak nonreciprocity promotes structural order while stronger asymmetry disrupts it. To capture these transitions, we introduce topological landscapes, mapping the distribution of structural motifs across state space. We further develop topological flowscapes, a dynamic framework that quantifies transitions between collective states and detects an informational rate shift and an emergent proofreading from the experimental state transition. Together, these results establish a general approach for decoding nonequilibrium transitions and uncover how asymmetric interactions sculpt the dynamical and structural architecture of active and living matter.

Pattern-forming dynamics govern the behavior of many quantum, electrochemical, and soft-matter systems, yet learning and controlling the corresponding partial differential equation (PDE) models on realistic geometries remains challenging. In this work, we develop a unified, differentiable framework for free-energy-based PDEs that enables end-to-end parameter inference and optimal control directly on image-based domains. Starting from a variational description in terms of an energy or free energy functional, we combine PDE-based smoothing of segmented geometries, the smoothed boundary method, advanced integrators for stiff pattern-forming PDEs, and memory-efficient automatic differentiation implemented in JAX to construct scalable PDE solvers amenable to gradient-based optimization. We demonstrate the capabilities of this framework across four classes of applications: (1) learning Cahn-Hilliard and Allen-Cahn free energies and kinetic laws from noisy spatiotemporal data on complex battery electrode microstructures; (2) designing time-dependent wetting boundary conditions that steer phase boundaries to desired orientations; (3) optimizing spatially varying reaction rates, interpreted as surface coatings, to suppress phase separation in intercalation electrode models; and (4) computing time-dependent trapping potentials that transfer Bose-Einstein condensates between ground states of qualitatively different Gross-Pitaevskii potentials while minimizing excitations. Together, these results show that variational PDE models, when equipped with differentiable solvers on complex domains, provide a versatile substrate for data-driven discovery, design, and control of pattern-forming materials and quantum fluids, and they point toward tighter integration of physics-based PDE modeling with modern optimization and machine learning pipelines.

Mosquito-borne diseases cause several hundred thousand deaths worldwide every year. Deciphering mosquito host-seeking behavior is essential to prevent disease transmission through mosquito capture and surveillance. Despite recent substantial progress, we still lack a comprehensive quantitative understanding of how visual and other sensory cues guide mosquitoes to their targets. Here, we combined three-dimensional infrared tracking of Aedes aegypti mosquitoes with Bayesian dynamical systems inference to learn a quantitative biophysical model of mosquito host-seeking behavior. Trained on more than 20 million data points, each corresponding to an instantaneous position and velocity in mosquito free-flight trajectories recorded in the presence of visual and carbon dioxide cues, the model accurately predicts how mosquitoes respond to human targets. Our results provide a quantitative foundation for optimizing mosquito capture and control strategies, a key step toward mitigating the impact of mosquito-borne diseases.

During development, highly ordered structures emerge as cells collectively coordinate with each other. While recent advances have clarified how individual cells process and respond to external signals, understanding collective cellular decision making remains a major challenge. Here, we introduce a minimal, analytically tractable model of cell patterning via local cell-cell communication. Using this framework, we identify a trade-off between the speed and accuracy of collective pattern formation and, by adapting techniques from stochastic chemical kinetics, quantify how information flows between cells during patterning. Our analysis reveals counterintuitive features of collective patterning: globally optimized solutions do not necessarily maximize intercellular information transfer and individual cells may appear suboptimal in isolation. Moreover, the model predicts that instantaneous information shared between cells can be nonmonotonic in time as patterning occurs. An analysis of recent experimental data from lateral inhibition in pupal abdomen finds a qualitatively similar effect.

Regulation of cell growth and division is essential to achieve cell-size homeostasis. Recent advances in imaging technologies, such as “mother machines” for bacteria or yeast, have allowed long-term tracking of cell-size dynamics across many generations, and thus have brought major insights into the mechanisms underlying cell-size control. However, understanding the governing rules of cell growth and division within a quantitative dynamical-systems framework remains a major challenge. Here, we implement and apply a framework that makes it possible to infer stochastic-differential-equation models with Poisson noise directly from experimentally measured time series for cellular growth and division. To account for potential nonlinear memory effects, we parameterize the Poisson intensity of stochastic cell-division events in terms of both the cell’s current size and its ancestral history. By applying the algorithm to experimentally measured cell-size trajectories, we are able to quantitatively evaluate the linear one-step memory hypothesis underlying the popular “sizer,” “adder,” and “timer” models of cell homeostasis. For Escherichia coli and Bacillus subtilis bacteria, Schizosaccharomyces pombe yeast and Dictyostelium discoideum amoebae, we find that in many cases, the inferred stochastic models have a substantial nonlinear memory component. This suggests a need to reevaluate and generalize some of the currently prevailing linear-memory paradigms of cell homeostasis. More broadly, the underlying inference framework is directly applicable to identify quantitative models for stochastic jump processes in a wide range of scientific disciplines.

Most animals coordinate behaviour using neural computations. Yet, single-celled organisms also exhibit stimulus-responsive, even cognitive, actions. To understand how a single cell can coordinate and drive complex behaviours without any neural encoding, we study an algal protist – a motile cell with four extremely long cilia. The organism displays a surprisingly rich locomotor repertoire, emerging from the intricate dynamics of the cilia, which form a tight bundle when swimming. We leverage high-speed quantitative live imaging to extract the spectrum of possible ciliary beating patterns, and derive a dispersion relation coupling the temporal frequency and spatial wavelength of cilia oscillations. We further reconstruct the attractor manifold embedded in the behavioural space, showing that despite the range and complexity of ciliary beating modes, the underlying behavioural manifold is intrinsically low-dimensional with elaborate topological structure. Dynamic and excitable transitions in motility behaviour are encoded as trajectories in this space.

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media. Published by the American Physical Society 2025

Mosquito-borne diseases cause several hundred thousand deaths every year. Deciphering mosquito host-seeking behavior is essential to prevent disease transmission through mosquito capture and surveillance. Despite recent substantial progress, we currently lack a comprehensive quantitative understanding of how visual and other sensory cues guide mosquitoes to their targets. Here, we combined 3D infrared tracking of Aedes aegypti mosquitoes with Bayesian dynamical systems inference to learn a quantitative biophysical model of mosquito host-seeking behavior. Trained on more than 20,000,000 data points from mosquito free-flight trajectories recorded in the presence of visual and carbon dioxide cues, the model accurately predicts how mosquitoes respond to human targets. Our results provide a quantitative foundation for optimizing mosquito capture and control strategies, a key step towards mitigating the impact of mosquito-borne diseases.

Despite rapid progress in data acquisition techniques, many complex physical, chemical, and biological systems remain only partially observable, thus posing the challenge to identify valid theoretical models and estimate their parameters from an incomplete set of experimentally accessible time series. Here, we combine sensitivity methods and ranked-choice model selection to construct an automated hidden dynamics inference framework that can discover predictive nonlinear dynamical models for both observable and latent variables from noise-corrupted incomplete data in oscillatory and chaotic systems. After validating the framework for prototypical FitzHugh-Nagumo oscillations, we demonstrate its applicability to experimental data from squid neuron activity measurements and Belousov-Zhabotinsky reactions, as well as to the Lorenz system in the chaotic regime. Published by the American Physical Society 2024

We describe a general procedure for mapping arbitrary n -qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multiqubit states find natural field representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor's algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and nonstandard computation. Published by the American Physical Society 2024